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Columns: Finding the Strongest Shape

The shapes of a structure and its parts are often as important as the materials those parts are made of. In this video segment adapted from ZOOM, members of the cast bend and fold sheets of paper to see which shape is strongest and can best support the weight of a heavy book. This resource is useful for introducing components of Engineering Design (ETS) from the Next Generation Science Standards (NGSS) to grade K-8 students.

Columns are among the oldest and most effective building elements for resisting the pushing, or compression, that takes place in all kinds of structures. Paired with horizontal beams, these critical forms can carry the weight of an entire structure. Still, each column has its limits, and some types perform far better than others.

Columns can fail, or collapse, in two ways: by crushing and by buckling. Crushing results when the weight of a well-distributed load simply exceeds the compressive strength of the material from which the column is made. Because columns are usually constructed from dense materials such as stone, concrete, or steel, this type of failure is relatively uncommon.

Columns usually fail because of instability, rather than lack of strength. Assuming that a column is attached to a solid foundation, stability is usually related to the column's dimensions. Shorter, thicker columns are far more stable than long, slender columns. Like short, thick horizontal beams, shorter, thicker columns are more resistant to bending than are slender columns, and a column that resists bending also resists buckling.

Shape also plays an important role in a column's stability. The cylinder is one of the most widely used shapes in column construction. This is because the cylinder's circular cross section places the column's material and its outer boundary at a consistent distance from the center, so the column has no side that is weaker -- and thus more susceptible to buckling -- than any other.

Finally, proper placement of a load is critical to the stability of a column. The more closely a load is applied to the center of the top of a column, the more stable that column will be. As a load moves away from the center of a column, the side of column to which the load shifts takes on more and more of the load. Such an unbalanced load can cause a column to bend in the same way that an overloaded beam bends, which may lead to buckling.

What shape of bent or rolled paper best supports a book? Use this experiment to help students understand the steps of engineering design. You can either use the video directly with your students, or recreate the activity and then have your students take it on. In either case, emphasize the engineering design steps involved.

Before watching the video: Show students a piece of paper and ask if they think it is strong enough to hold a book up off a table. After students share thoughts, start the video.

While watching the video: Pause the video at 0:24 and ask the same question: “What do you think will happen?” After this discussion, which doesn’t require correct answers — just predictions — ask students to describe the goal of the different shapes of paper. To hold up the books. Students identify the problem, part of the Engineering Practice, Defining Problems. Watch the next portion of the video, up until the cast members are about to test the shapes at 0:45, and pause the video again. Did the thoughts of the two kids in the video match those of your students? The two kids kept the four different shapes on the table to look at as they thought about what might or might not be successful in their design. Why are these shapes important? They are physical models that represent potential solutions. Students recognize that physical models are useful in communicating ideas to other people, part of the Engineering Practice, Developing and Using Models. Finish watching the video.

After watching the video: Have the students discuss the testing results. Did they turn out as predicted? Why was it good to actually do the tests and not just think about what might happen? Students recognize that it is useful to compare and test designs, part of the Engineering Practice, Analyzing and Interpreting Data.

What shape of bent or rolled paper best supports a book? Use this experiment to help students understand the steps of engineering design. You can either use the video directly with your students, or recreate the activity and then have your students take it on. In either case, emphasize the engineering design steps involved.

Before watching the video: Show students a piece of paper and ask if they think it is strong enough to hold a book up off a table. After students share thoughts, start the video.

While watching the video: Pause the video at 0:24 and ask the same question: “What do you think will happen?” After this discussion, which doesn’t require correct answers — just predictions — ask students to describe the goal of the different shapes of paper and the constraints placed on the materials. A single sheet of paper needs to hold up book(s). Students identify the problem and constraints, part of the Engineering Practice, Defining Problems. Watch the next portion of the video, up until cast members are about to test the shapes at 0:45, and pause the video again. Did the thoughts of the two kids in the video match those of your students? The two kids kept the four different shapes on the table to look at as they thought about what might or might not be successful in their design. Why are these shapes important? They are physical models that represent potential solutions, which can be tested to see if they work. Students recognize that physical models are useful for testing, part of the Engineering Practice, Designing Solutions. Finish watching the video.

After watching the video: Have the students discuss the testing results. Did they turn out as predicted? Why was it good to actually do the tests, using a single sheet of paper for each shape? Students recognize that it is useful to control variables while testing designs, part of the Engineering Practice, Planning and Carrying Out Investigations.

What shape of bent or rolled paper best supports a book? Use this experiment to help students understand the steps of engineering design. You can either use the video directly with your students, or recreate the activity and then have your students take it on. In either case, emphasize the engineering design steps involved.

Before watching the video: Show students a piece of paper and ask if they think it is strong enough to hold a book up off a table. After students share thoughts, start the video.

While watching the video: Pause the video at 0:24 and ask the same question: “What do you think will happen?” After this discussion, which doesn’t require correct answers — just predictions — ask students to describe the goal of the different shapes of paper and the constraints placed on the materials. A single sheet of paper needs to hold up book(s). Students identify the problem and constraints, part of the Engineering Practice, Defining Problems. Finish watching the video.

After watching the video: Have the students discuss the testing results. Did they turn out as predicted? What design features in the solutions proved most successful? Students construct arguments to support or refute claims, part of the Engineering Practice, Engaging in Argument from Evidence.

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